What is the slope of the line normal to the tangent line of #f(x) = e^(x-2)+x-2 # at # x= 2 #?
In this case, the slope of the tangent line will be given by
The normal line is the line perpendicular to the tangent line; therefore, its slope will be the negative reciprocal of the slope to the tangent line, or,
Let's first differentiate the function:
Determine the slope of the tangent:
The slope of the normal line is then